MicrotonalTheory

Contents

Theory: Inventions that shape understanding

Theories are not discoveries but inventions of humans, usually meant to formally describe regularities in experience, which often bring forth new ways of experiencing. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories; it is thus important to recognize that theory and practice mutually and reciprocally influence each other.)

There is a great deal of theory around the creation and/or discovering of tunings, scales, and temperaments, but whether it is useful to bother learning any of them is a matter of personal decision. (It is always possible to load up a random tuning on your retunable instrument of choice and explore it through music, without bothering to understand the theoretical considerations that led to the construction and/or discovery of said tuning.) Below you will find a partial list of currently-established theories related to alternative intonations.

Regular Temperaments (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires

Moment of Symmetry, a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson

Graham complexity, a complexity measure which works well with MOS scales and rank two regular temperaments.

Empirical This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.